A study into the use of the Solution Combustion Synthesis (SCS) method with glycine and citric acid to synthesize fine powders of multicomponent solid solutions of oxides of rare earth (RE) metals (Nd, Sm, Eu, Gd, Dy, and Ho) for the preparation of ceramic materials is presented. Synthesis parameters of 4-, 5-, and 6-component entropy-stabilized rare earth oxides (REOs) with a C-type cubic structure are determined. The stability of entropy-stabilized oxides (ESOs) with a C-type structure is shown to depend not only on heavy RE metal quantity, but also on the rate of heating/cooling of the samples. The temperature of the polymorphic transformation of C-type REO structures into B-type (monoclinic) or H-type (hexagonal) structural variants can be described by the equation T (°C) = 0.0214Vcr2 − 62.737Vcr + 46390, where Vcr is the unit cell volume of an oxide with a C-type structure regardless of the number of cations in the solid solution. High-temperature thermal analysis up to 1250 °C revealed that dispersed powders, which contain impurities of basic carbonates along with hydroxocarbonates of RE metals and X-ray amorphous carbon formed during SCS reactions, also react with air moisture during storage. The influence of the ESO phase and cationic composition on the morphology, porosity and microhardness of ceramics was studied. Higher-entropy oxides form samples with higher density, microhardness and a smaller size of particle agglomerates.